Here, we demonstrate the use of the X-ray fluorescence fitting software, MAPS, created by Argonne National Laboratory for the quantification of fluorescence microscopy data. The quantified data that results is useful for understanding the elemental distribution and stoichiometric ratios within a sample of interest.
The quantification of X-ray fluorescence (XRF) microscopy maps by fitting the raw spectra to a known standard is crucial for evaluating chemical composition and elemental distribution within a material. Synchrotron-based XRF has become an integral characterization technique for a variety of research topics, particularly due to its non-destructive nature and its high sensitivity. Today, synchrotrons can acquire fluorescence data at spatial resolutions well below a micron, allowing for the evaluation of compositional variations at the nanoscale. Through proper quantification, it is then possible to obtain an in-depth, high-resolution understanding of elemental segregation, stoichiometric relationships, and clustering behavior.
This article explains how to use the MAPS fitting software developed by Argonne National Laboratory for the quantification of full 2-D XRF maps. We use as an example results from a Cu(In,Ga)Se2 solar cell, taken at the Advanced Photon Source beamline 2-ID-D at Argonne National Laboratory. We show the standard procedure for fitting raw data, demonstrate how to evaluate the quality of a fit and present the typical outputs generated by the program. In addition, we discuss in this manuscript certain software limitations and offer suggestions for how to further correct the data to be numerically accurate and representative of spatially resolved, elemental concentrations.
Synchrotron-based XRF has been used across multiple disciplines for many decades. For example, it has been used in biology on studies such as that done by Geraki et al., in which they quantified trace amounts of metal concentrations within cancerous and non-cancerous breast tissue 1. More generally, quantitative XRF has been applied to a wide array of biology studies concerned with metal concentrations in cells and tissues, as described by Paunesku et al.2. Similarly, marine protists were studied for trace elements 3,4 and even micro- and macronutrient distributions were observed within plant cells 5. Work by Kemner et al.6, which identified distinct differences in morphology and elemental composition in single bacteria cells, was also made possible through quantitative XRF analysis. Additionally, and specifically relevant to the example disclosed herein, materials scientists studying solar cell devices have made use of high-resolution XRF for studies on the existence of sub-micron metal impurities in silicon semiconductors 7,8, correlative work on how elemental distributions affect electrical performance in solar devices 9,10, and identifying depth-dependent gradients of CIGS thin film solar cells via grazing incidence X-ray fluorescence (GIXRF) 11.
Many of these studies make use not only of the high-resolution capabilities of synchrotron X-ray fluorescence to study spatial distribution, but also the quantification of the information for drawing numerical conclusions. In many studies it is critical to know the elemental concentrations associated with the aforementioned spatial distributions. For instance, in the work by Geraki et al., the study required quantifying the difference in concentrations of iron, copper, zinc, and potassium in cancerous and non-cancerous breast tissues, to better understand what concentrations become harmful to human tissues 1. Similarly, work by Luo et al. made use of quantified XRF to identify small amounts of chlorine incorporated in perovskite solar cells when synthesized both with and without chlorine-containing precursors 12. Therefore, for certain studies in which the concentrations of elements are needed, proper quantification is a necessary and critical step.
The process of quantifying elemental concentrations from X-ray fluorescence (XRF) measurements translates fluorescence intensity counts into mass concentrations (e.g. µg/cm2). The raw spectra present the number of photons collected by the energy dispersive fluorescence detector as a function of energy. The spectra are first fit and then compared to a standard measurement to calculate the quantified data. In particular, the first step of fitting fluorescence spectra is critical even for the qualitative analysis of the elements. This is because prior to fitting, counts are binned based on their energy, which becomes a problem when two elements with similar fluorescence transitions are contained in the sample. In this situation, counts may be incorrectly binned and thus associated with the wrong element.
It is often also necessary to quantify XRF spectra in order to accurately draw conclusions on relative quantities of elements in a sample. Without proper quantification, counts of heavy elements and lighter elements will be compared directly, ignoring differences in capture cross section, absorption and fluorescence probability, attenuation of the fluorescence photons, and the distance of the element's absorption edge from the incident energy, which all affect the number of photons striking the detector. Therefore, the process of fitting the spectra for each map and comparing peak intensities to the standard, both of which are done in the following procedure, is critical for the accurate quantification of each of the elemental concentrations.
We demonstrate how to convert the raw counts of fluorescence photons to units of micrograms per square centimeter (µg/cm2) by first fitting an integral spectrum, or a summed spectrum of all the individual spectra produced at each measurement spot or pixel in a 2D map. This spectrum demonstrates the relative intensities of the different elements contained in the sample. The distance the absorption edge of a certain element is from the incident beam energy influences the intensities of their fluorescence peaks. In general, the closer the two energies are, the greater the intensity produced for those elements, although this is not always the case. Figure 4 in Ref 13 shows the dependence of the absorption length of X-ray photons, which directly relates to the resulting intensity, for the majority elements in a methylammonium lead iodide perovskite solar cell. This demonstrates the fluorescence response of elements with respect to energy, and shows that it is not a continual decrease in response with increasing distance from the incident energy, but rather that it is also dependent upon the element itself.
The result of this relationship is that raw elemental concentrations may appear higher for element channels with excitation energies closer to the incident energy, even if the true quantities of those elements are lower in relation to other elements with excitation energies farther from the incident. Therefore, the energy dependence of intensity, along with other factors such as fluorescence yield variations, different absorption edges, detector sensitivity, and measurement background, etc., is why fitting the data is very important prior to drawing conclusions on the observed elemental quantities. We then apply a fitting algorithm to the integral spectrum, where the user defines the elements and parameters to fit via a text document.
The algorithm, created by Vogt et al. 14, makes use of regions of interest (ROI) filtering, in which it integrates over certain elements' peak regions, and principle component analysis (PCA). First, PCA is done to identify only the elements and peaks that are very strongly apparent. This allows for the separation of noise from the true signal. Next, the principle components identified are numerically quantified, which is important for deconvoluting different element peaks with the same excitation energy, for example overlapping Au Mα and P Kα. Finally, ROI filtering may be applied to the numeric data by integrating over specified regions.
To relate counts to elemental concentrations, a well-quantified reference (often referred to as "standard") is measured under the same measurement conditions, geometry and energy, as the sample under study. This standard is often from Dresden AXO or from the National Institute of Standards and Technology (NIST). They cover a variety of different elements and come with tabulated elemental distributions. The normalization of the measured counts of the sample of interest to the counts of the standard under the same measurement conditions provides the basis for the elemental quantification for the sample of interest.
More specifically, MAPS identifies the elements and their concentrations of the standard either by the fact that the standard information is known by the program (as is the case for the AXO and NIST standards) or through data entered into a separate file (in the case of a different standard being used). From this information, the program relates the measured intensities of the standard elements under the measurement settings to the anticipated concentration embedded in MAPS. It then creates a scaling factor to adjust for any offset and extrapolates this scaling factor to all the remaining elements not included in the standard. The scaling factor then includes the offset from the measurement settings and the information provided within MAPS for the linear conversion of raw counts to areal density in µg/cm2.
Here, we demonstrate how to make use of the program, MAPS, developed by Dr. S. Vogt, to quantify data acquired from fluorescence-capable beamlines at Argonne National Laboratory (ANL) 14. The data used for the demonstration was acquired at sector 2-ID-D of ANL using the measurement setup shown in Figure 1 of 10. The fitting procedure may also be applied to data taken from other beamlines, however, note that certain characteristics of the ANL beamlines are embedded in the program and will need to be updated.
NOTE: Prior to beginning the fitting, it is important to know a few things about the measurements taken: the number of detector elements used – different beamlines use different detectors which are sometimes segmented into smaller sections from which the counts are read and compiled; the incident energy used; and the standard measured. This information will be applied throughout different aspects of the procedure.
1. Setting up the program
2. Performing the fitting
3. Run the fitting
4. Checking the fit
An example of proper fitting results can be seen in the following Figures. Firstly, in Figure 1 a direct comparison is shown between a poor fit and a good fit for the integral spectrum. The bad fit is reparable by both ensuring no elements are missing, for instance copper, which has a clear peak in Figure 1(left) but is not being included in the fit, and adjusting the branching ratios of the L and K lines to improve the accuracy. Figure 2 instead shows a comparison between the element channels before and after fitting. The first noticeable difference is the units for the values changes from "raw" to "ug/cm^2", suggesting that the data have been quantified. Additionally, number ranges should align with those expected from the suggested calculation in section 4.2. These values should generally not go to zero. If they do, this is almost always a sign that there is an error in the fitting.
Both the iron and copper channels can be seen both before and after the fitting. Beyond observing the value changes, it is also clear that the images are better resolved and the stripes that appear in the raw data are gone upon fitting. This resolution increase comes as a result of the peak deconvolution done by the fitting for the separation of elements with overlapping peaks. It is just one of the benefits of fitting and quantifying the data, providing the ability to more accurately qualitatively and quantitatively analyze the fluorescence data. In the particular example of a CIGS solar cell, one of the properties that researchers are interested in is the distribution of the three cations, copper, indium, and gallium, throughout the device. Statistical research has been done to study the change in their concentrations within grains and grain boundaries 16. Such a study requires the improved resolution within the map so that boundaries can be more easily identified using a watershed technique. Additionally, having the capability to study the correlation and anti-correlation of the elements provides an outlook on sample homogeneity and how to improve it.
While the quantified data can now be used to relate elemental concentrations, the fitting procedure is not perfect. There will always be a degree of error introduced from the various procedure steps, including, but not limited to, the quality of the fit, the selection, matrix homogeneity, measurement, and extrapolation of the standard, and the influence of other factors such as secondary fluorescence and sample thickness variation that are not taken into consideration by MAPS. These errors can be minimized by selecting a homogenous standard with multiple common elements with the sample and improving branching ratios as much as possible, however, note that some of these, such as controlling fit quality, are systematic errors that are hard to eradicate completely. Although it is not possible to directly quantify the error incurred, purchased standards will provide an error estimation for the concentrations of the elements, which are often quite high and should be considered when trying to analyze and propagate errors.
Correcting the data further for certain issues such as thickness variation, beam attenuation, and secondary fluorescence can help reduce the error even further. Methodologies available to do such corrections are described in the discussion section.
Figure 1. Demonstration of before (left) and after (right) the proper adjustments have been made to the fitting file to produce an accurate fitting (shown in green) of the integral spectrum (shown in white) and later, to convert raw counts to µg/cm2 accurately. Two common types of error are circled in (a): the red circle identifies a missing element, in this case Cu, and the yellow circle identifies a problem with the branching ratios for the In_L line. Please click here to view a larger version of this figure.
Figure 2. Demonstration of before (top) and after (bottom) fitting and quantification of the fluorescence channels of interest. Most notable is the change in units from "raw" to "ug/cm^2". The quantified values for iron and copper in a 2 µm thick CIGS solar cell on a 500 µm thick stainless steel substrate are on the order of 1000 and 100 µg/cm2.
The figures show the importance of fitting data using this procedure. Figures 1 (right) and 2 (bottom) show a representative result that should arise from a proper fitting. If there is an insufficient fit, the integral spectrum image will look noticeably off and the resulting quantified data will have errors in it, although these will be hard to detect in most cases. For certain sample types for which the standard is not representative of the elements in the sample, particularly in that the samples do not contain any of elements in the standard, the quantification relies solely on extrapolating information for all the elements of interest. In a situation like this, the fitting will appear to be accurate when analyzed using the integral spectrum, however, upon quantifying, the values will appear dramatically incorrect. In this situation, it becomes necessary to use a standard of known quantities that is more similar to the sample. The process of choosing and comparing standards is well demonstrated in a study by Twining et al., which made use of the NIST standard, as well as some synthesized standards, for quantifying biological samples 3. By doing so, the authors were able to verify the appropriateness of each standard and compare the areal densities produced by using each standard for the fitting. Most importantly, the paper shows the reduction of error that results from choosing an appropriate standard and oppositely, the strong impact that using the wrong standard can have on quantification.
In addition to the fitting and quantification, there are other corrections that can be done to ensure the accurate interpretation of quantified data produced by XRF. One example is described by West et al. 20, which uses attenuation calculations provided by DeBoer 21 to further correct the quantified data for thickness variations and beam attenuation within a multi-layer sample. The article uses CIGS thin film solar cells in a case study for demonstrating the importance of using such attenuation corrections prior to forming conclusions on the observed concentration variations. The correction addresses the issue that in a multilayer sample with assumed thickness variation within the layers, regions prior to correction may suggest higher relative quantities of a certain element due to increased thickness rather than increased elemental concentration. The correction also accounts for beam attenuation of the incoming and outgoing beam in multilayer samples, as well as self-attenuation of elements within the specific layer of interest. This is one example of additional analysis necessary for the accurate quantification of X-ray fluorescence microscopy data. However, the corrections applied in 20 are based on assumptions that do not hold for all types of samples, and further corrections may need to be considered depending on the sample material and structural characteristics.
It is important to note that the raw and fitted data also include counts from secondary fluorescence occurring from fluorescence photons of one element providing enough energy to produce fluorescence photons of other elements with lower binding energies 21,22. The isolation of primary fluorescence photons from others is not possible by the fitting program, resulting in over- and under-quantification of certain elements. More specifically, the elements with higher fluorescence energies provide energy to elements of lower binding energy and are therefore not counted by the detector. Meanwhile, the atoms being excited by secondary fluorescence photons may be counted more than once because they first release photons due to the incident beam and then again release photons from the other sample elements. The data, therefore, requires additional treatment if these interactions are anticipated to have a significant impact on the quantification of elements of interest. Currently, the best approach for handling secondary fluorescence is through modeling and estimating the yield, such as what is described in 23. Information on the regime over which secondary fluorescence becomes significant and additional equations for estimation are provided in 22.
This work has demonstrated the first steps necessary for the quantification of X-ray fluorescence data. Although the process still requires many improvements and issues can arise that are specific to the type of sample studied (semiconductors, plant cells, human tissues, etc.), the technique is a reliable method for extracting meaningful quantitative information from the qualitative raw data acquired from XRF measurements.
The authors have nothing to disclose.
We acknowledge funding from the U.S. Department of Energy under contract DE-EE0005948. Use of the Center for Nanoscale Materials and the Advanced Photon Source, both Office of Science user facilities, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. This material is based upon work supported in part by the National Science Foundation (NSF) and the Department of Energy (DOE) under NSF CA No. EEC-1041895. Video editing was done by VISLAB at Arizona State University. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect those of NSF or DOE. T.N. is supported by an IGERT-SUN fellowship funded by the National Science Foundation (Award 1144616).